# American Institute of Mathematical Sciences

December  2012, 2(4): 331-359. doi: 10.3934/mcrf.2012.2.331

## Carleman inequalities for the two-dimensional heat equation in singular domains

 1 Faculté de Mathématiques, laboratoire AMNEDP, U.S.T.H.B, B.P. 32, El-Alia, 16111 ALGER, Algeria, Algeria, Algeria, Algeria

Received  January 2012 Revised  May 2012 Published  October 2012

We consider the Cauchy problem associated to the heat equation firstly in a plane domain with a reentrant corner, then in a cracked domain. By constructing a weight function, we prove a Carleman inequality and we deduce a result of controllability.
Citation: Abdelhakim Belghazi, Ferroudja Smadhi, Nawel Zaidi, Ouahiba Zair. Carleman inequalities for the two-dimensional heat equation in singular domains. Mathematical Control & Related Fields, 2012, 2 (4) : 331-359. doi: 10.3934/mcrf.2012.2.331
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